Magneto-mechanical deformation of \ch{Ni50Mn28Ga22} shape memory alloy

This study deals with pseudoplastic deformation of Ni50Mn28Ga22 alloy exhibiting mechanically and magnetically induced crystal reorientation. The new approach was introduced, taking into account crystals with single initial variant as well as nucleation of different orientation. Initially, observations from optical microscope and AFM (atomic force microscope) were correlated with the mechanical measurements from stress-strain machine to characterize boundaries between crystal variants. These observations were subsequently used to clarify the results of the mechanical deformation tests. By magnetizing samples in VSM (vibrating-sample magnetometer), analogous magnetic measurements to mechanical tests were conducted. The two types of measurements were then compared with respect to energy. The discrepancy found between the model and measurements is in agreement with previous studies. Some experimental factors and possible errors that may affect measurement have been discussed. Nevertheless, the observed differences remain an unresolved issue suggesting a need for a modification of the model.

Solving Diophantine Equations by Factoring in Number Fields

In this text we provide an introduction to algebraic number theory and show its applications in solving certain difficult diophantine equations. We begin with a quick summary of the theory of quadratic residues, before diving into a select few areas of algebraic number theory. Our article is accompanied by a couple of worked problems and exercises for the reader to tackle on their own.

Impact of the Economic Impact Payments on Consumer Spending:\\ Analysis on a Granular Level of American Counties

This paper draws on weekly consumer spending data collected by American private companies to analyze the impact of the Economic Impact Payments on consumer spending in American counties. We use regression discontinuity design to quantify the causal effect of the Stimulus Checks on spending and use heterogeneity in economic and demographic factors to determine which groups of counties increased their spending the most, to see what factors affected the Stimulus Checks’ effectiveness. We then use the observed difference in impact across groups of counties to discuss whether the Stimulus Checks were the optimal governmental policy in the crisis and discuss the effectiveness of one-time transfer payments in future recessions.

A Pseudorandom Sequence Generated over a Finite Field Using The Möbius Function

The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $\mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $\mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.

Miloslav Frumar: In the footsteps of the chalcogenide semiconductors

The year 2021 is the year of the 85th anniversary of the birth of Professor Miloslav Frumar the enthusiastic chemist who dedicated his whole professional life to the study of amorphous and glassy chalcogenides which are used in numerous applications like copying machines, laser printers, DVDs or memories.